I am a newbie so grain of salt and etc...
Left to right:
The stamping on the tweezers indicates what model it is. It seems like the letters and numbers are standard among manufactures. I looked up "C" and nothing came up. I could be that the watchmaker grind a spare tweezer for a special purpose. Maybe holding pivots?
No idea. I seen that on Ebay listing so it's probably another wacky looking watch tool.
No idea. I am guessing that the collar on the tool slides on the arms to tighten on a pinion. It's basically a pin vise.
This is probably to heat up pieces to put shellac on it. You put the brass plate over a flame and put the shellac on it. You attach jewels in way.
This funny looking tool is a holder for the roller impulse jewel on the balance staff. People use this tool to replace the impulse on very old pocket watches where parts are extremely scarce. This blog post showcases the usage of two of your tools.
I don't know about the last two. Looks like some sort of holder for a part.
For the first picture, it looks like something you put pinions into to true a wheel. Although it missing the upper half if that's the case. Maybe it's part of a staking set and it holds parts with pinions?
For the second picture, I agree. It does look like center punches. You can easily figure that out by using it.